Comparisons of statistical distributions for cluster sizes in a developing pandemic

BACKGROUND

We consider cluster size data of SARS-CoV-2 transmissions for a number of different settings from recently published data. The statistical characteristics of superspreading events are commonly described by fitting a negative binomial distribution to secondary infection and cluster size data as an alternative to the Poisson distribution as it is a longer tailed distribution, with emphasis given to the value of the extra parameter which allows the variance to be greater than the mean. Here we investigate whether other long tailed distributions from more general extended Poisson process modelling can better describe the distribution of cluster sizes for SARS-CoV-2 transmissions.

METHODS

We use the extended Poisson process modelling (EPPM) approach with nested sets of models that include the Poisson and negative binomial distributions to assess the adequacy of models based on these standard distributions for the data considered.

RESULTS

We confirm the inadequacy of the Poisson distribution in most cases, and demonstrate the inadequacy of the negative binomial distribution in some cases.

CONCLUSIONS

The probability of a superspreading event may be underestimated by use of the negative binomial distribution as much larger tail probabilities are indicated by EPPM distributions than negative binomial alternatives. We show that the large shared accommodation, meal and work settings, of the settings considered, have the potential for more severe superspreading events than would be predicted by a negative binomial distribution. Therefore public health efforts to prevent transmission in such settings should be prioritised.

Markov Chain Modelling for Geriatric Patient Care

Objectives: To show that Markov chain modelling can be applied to data on geriatric patients and use these models to assess the effects of covariates.

Methods: Phase-type distributions were fitted by maximum likelihood to data on times spent by the patients in hospital and in community-based care. Data on the different events that ended the patients’ periods of care were used to estimate the dependence of the probabilities of these events on the phase from which the time in care ended. The age of the patients at admission to care and the year of admission were also included as covariates.

Results: Differential effects of these covariates were shown on the various parameters of the fitted model, and interpretations of these effects made.

Conclusions: Models based on phase-type distributions were appropriate for describing times spent in care, as the ordered phases had an interpretable structure corresponding to increasing amounts of care being given.

Bounds on the velocity of spread of infection for a spatially connected epidemic process

The simple (non-spatial) stochastic epidemic is generalised to allow infected individuals to move forward through a system of spatially connected colonies C1, C2, C3, ·· ·each containing susceptible individuals. Upper and lower bounding processes are considered, to establish bounds on the asymptotic velocity of forward spread of the infection through these spatially connected colonies. These bounds are shown to be asymptotically equivalent under certain conditions, and some simulations reveal other features of the process.

The outcome of a general spatial epidemic on the line

The general (non-spatial) stochastic epidemic is extended to allow infective individuals to move forward through a system of spatially connected locations · ··, L1, L2, · ·· (on the line) each containing susceptible individuals and the outcome of the epidemic in each of these locations is then considered. In the deterministic case, a (spatial) equilibrium solution and threshold behaviour are discussed. In the stochastic case, a (spatial) quasi-equilibrium behaviour (conditional on sufficient numbers of infectives present) is discussed; numerical results suggest some correspondence between this stochastic quasi-equilibrium and the deterministic equilibrium.

Optimal control of finite dams: discrete (2-stage) output procedure

The problem discussed is that of determining optimal release rates for finite dams when the release rate may take one of two values and specific costs are involved in increasing and decreasing this release rate. From another point of view, this is a problem of controlling the output simply by switching on and off. A diffusion model is suggested and by considering a family of plausible output policies an optima procedure, which minimises the long-term average cost of operating the dam, is established. Various properties of this output policy are given.

On variation in birth processes

Birth processes with piecewise linear birth rates are analysed, and numerical results suggest that, relative to the linear case, convex birth rates increase variability and concave birth rates decrease variability.

Optimal control of finite dams: continuous output procedure

The problem discussed is that of controlling optimally the release of water from a finite dam, when the release rate may vary continuously and the optimality is defined in terms of a cost structure imposed on the operation of the dam. A diffusion model is suggested and by considering a family of plausible output policies, the control problem is reduced to the solution of a free boundary problem associated with a certain partial differential equation. A set of necessary conditions for the optimal choice of these boundaries is established and a method of solution is suggested. By using this method, together with well-established computational techniques, numerical solutions are obtained. These numerical solutions indicate that this optimal policy does not result in very much improvement over a much simpler policy where the output rate is constrained to take only two values.

Stochastic compartmental models as approximations to more general stochastic systems with the general stochastic epidemic as an example

A general time-dependent stochastic compartmental model is considered, where particles may move between a set of m compartments or out of the system, and new particles may be introduced into the compartments by immigration. A simple argument not relying on generating function techniques is given for the solution of such a system. It is then demonstrated that this class of compartmental models can be used as approximations to more complex stochastic systems by replacing dependence on certain stochastic variables by dependence on corresponding deterministic variables, with some recent examples being discussed. A compartmental approximation to the general stochastic epidemic is then constructed which appears on the basis of some simulations to compare favourably with the true process, particularly after the infection has got established in the population.

Influence of a triclosan toothpaste on periodontopathic bacteria and periodontitis progression in cardiovascular patients: a randomized controlled trial

BACKGROUND AND OBJECTIVE

Triclosan/copolymer toothpaste is effective in controlling plaque and gingivitis and in slowing the progression of periodontitis. This study describes its influence on microbiological and clinical outcomes, over a 5-year period, in patients with established cardiovascular disease (CVD).

MATERIAL AND METHODS

Four-hundred and thirty-eight patients were recruited from the Cardiovascular Unit at The Prince Charles Hospital, Brisbane, Australia, and randomized to triclosan or placebo groups. Six sites per tooth were examined annually for probing pocket depth and loss of attachment. These outcomes were analysed, using generalized linear modelling, in 381 patients who had measurements from consecutive examinations. Concurrent load of the periodontal pathogens Aggregatibacter actinomycetemcomitans, Fusobacterium nucleatum, Tannerella forsythia and Porphyromonas gingivalis was determined, using quantitative real-time PCR, in 437 patients with baseline plaque samples. Group comparisons were expressed as geometric means. The chi-square test was used to test for differences between the two groups of patients with regard to the proportion of patients with different numbers of bacterial species.

RESULTS

There was no difference in general health or periodontal status between the groups at baseline. There was a significant reduction in the number of interproximal sites showing loss of attachment between examinations, by 21% on average (p < 0.01), in the triclosan group compared with the placebo group. The prevalence of patients with F. nucleatum and A. actinomycetemcomitans was high and remained relatively constant throughout the 5 years of the study. In contrast, the prevalence of T. forsythia and P. gingivalis showed more variability; however, there was no significant difference between the groups, at any time point, in the prevalence of any organism. A significant difference in the geometric means for P. gingivalis (p = 0.01) was seen at years 1 and 4, and for F. nucleatum (p = 0.01) and in the total bacterial load (p = 0.03) at year 2; however, these differences were not statistically significant following a Bonferroni correction for multiple comparisons. There was no difference between the groups in the geometric means for each organism at year 5.

CONCLUSION

Within the limitations of the study, these data suggest that the use of triclosan/copolymer toothpaste significantly slowed the progression of periodontitis in patients with CVD but that it had little influence on key subgingival periodontopathic bacteria in these patients over the 5 years of the study.

The Relationship Between Variation in Size of the Primordial Follicle Pool and Age at Natural Menopause

CONTEXT

Menopause has been hypothesized to occur when the nongrowing follicle (NGF) number falls below a critical threshold. Age at natural menopause can be predicted using NGF numbers and this threshold. These predictions support the use of ovarian reserve tests, reflective of the ovarian follicle pool, in menopause forecasting.

OBJECTIVE

The objective of the study was to investigate the hypothesis that age-specific NGF numbers reflect age at natural menopause.

DESIGN AND SETTING

Histologically derived NGF numbers obtained from published literature (n = 218) and distribution of menopausal ages derived from the population-based Prospect-European Prospective Investigation into Cancer and Nutrition (Prospect-EPIC) cohort (n = 4037) were combined.

PARTICIPANTS

NGF data were from single ovaries that had been obtained postnatally for various reasons, such as elective surgery or autopsy. From the Prospect-EPIC cohort, women aged 58 years and older with a known age at natural menopause were selected.

INTERVENTIONS

There were no interventions.

MAIN OUTCOME MEASURE(S)

Conformity between observed age at menopause in the Prospect-EPIC cohort and NGF-predicted age at menopause from a model for age-related NGF decline constructed using a robust regression analysis. A critical threshold for NGF number was estimated by comparing the probability distribution of the age at which the NGF numbers fall below this threshold with the observed distribution of age at natural menopause from the Prospect-EPIC cohort.

RESULTS

The distributions of observed age at natural menopause and predicted age at natural menopause showed close conformity.

CONCLUSION

The close conformity observed between NGF-predicted and actual age at natural menopause supports the hypothesis that that the size of the primordial follicle pool is an important determinant for the length of the individual ovarian life span and supports the concept of menopause prediction using ovarian reserve tests, such as anti-Müllerian hormone and antral follicle count, as derivatives of the true ovarian reserve.

The relationship between anti-Müllerian hormone in women receiving fertility assessments and age at menopause in subfertile women: evidence from large population studies

CONTEXT

Anti-Müllerian hormone (AMH) concentration reflects ovarian aging and is argued to be a useful predictor of age at menopause (AMP). It is hypothesized that AMH falling below a critical threshold corresponds to follicle depletion, which results in menopause. With this threshold, theoretical predictions of AMP can be made. Comparisons of such predictions with observed AMP from population studies support the role for AMH as a forecaster of menopause.

OBJECTIVE

The objective of the study was to investigate whether previous relationships between AMH and AMP are valid using a much larger data set.

SETTING

AMH was measured in 27 563 women attending fertility clinics.

STUDY DESIGN

From these data a model of age-related AMH change was constructed using a robust regression analysis. Data on AMP from subfertile women were obtained from the population-based Prospect-European Prospective Investigation into Cancer and Nutrition (Prospect-EPIC) cohort (n = 2249). By constructing a probability distribution of age at which AMH falls below a critical threshold and fitting this to Prospect-EPIC menopausal age data using maximum likelihood, such a threshold was estimated.

MAIN OUTCOME

The main outcome was conformity between observed and predicted AMP.

RESULTS

To get a distribution of AMH-predicted AMP that fit the Prospect-EPIC data, we found the critical AMH threshold should vary among women in such a way that women with low age-specific AMH would have lower thresholds, whereas women with high age-specific AMH would have higher thresholds (mean 0.075 ng/mL; interquartile range 0.038-0.15 ng/mL). Such a varying AMH threshold for menopause is a novel and biologically plausible finding. AMH became undetectable (<0.2 ng/mL) approximately 5 years before the occurrence of menopause, in line with a previous report.

CONCLUSIONS

The conformity of the observed and predicted distributions of AMP supports the hypothesis that declining population averages of AMH are associated with menopause, making AMH an excellent candidate biomarker for AMP prediction. Further research will help establish the accuracy of AMH levels to predict AMP within individuals.

Malaria antibody persistence correlates with duration of exposure

BACKGROUND AND OBJECTIVES

In Australia, the risk of transfusion-transmitted malaria is managed through the identification of 'at-risk' donors, antibody screening enzyme-linked immunoassay (EIA) and, if reactive, exclusion from fresh blood component manufacture. Donor management depends on the duration of exposure in malarious regions (>6 months: 'Resident', <6 months: 'Visitor') or a history of malaria diagnosis. We analysed antibody testing and demographic data to investigate antibody persistence dynamics. To assess the yield from retesting 3 years after an initial EIA reactive result, we estimated the proportion of donors who would become non-reactive over this period.

MATERIALS AND METHODS

Test results and demographic data from donors who were malaria EIA reactive were analysed. Time since possible exposure was estimated and antibody survival modelled.

RESULTS

Among seroreverters, the time since last possible exposure was significantly shorter in 'Visitors' than in 'Residents'. The antibody survival modelling predicted 20% of previously EIA reactive 'Visitors', but only 2% of 'Residents' would become non-reactive within 3 years of their first reactive EIA.

CONCLUSION

Antibody persistence in donors correlates with exposure category, with semi-immune 'Residents' maintaining detectable antibodies significantly longer than non-immune 'Visitors'.

Relationship of serum antimüllerian hormone concentration to age at menopause

BACKGROUND

Serum antimüllerian hormone (AMH) levels are highly correlated with antral follicle counts, while being menstrual cycle independent and easily measurable. However, AMH, unlike antral follicle counts, has not been tested as yet as a predictor of reproductive status. By relating AMH levels to the age distribution of reproductive events like onset of menopause, we tested this hypothesis.

METHODS

AMH levels were measured in 144 fertile normal volunteers and used to determine an estimate of mean AMH as a function of age. Data on the onset of menopause were obtained from the population-based Prospect-European Prospective Investigation into Cancer and Nutrition [Prospect-EPIC] cohort. Estimation of an AMH threshold to predict menopause was done by maximum likelihood using the observed (Prospect-EPIC) distribution of age at menopause and the predictive distribution from this AMH threshold. Predictions of age at menopause follow from an individual woman's AMH relative to percentiles of the distribution of AMH for a given age, and the corresponding percentiles of the predictive distribution of age at menopause.

RESULTS

There was good conformity between the observed distribution of age at menopause and that predicted from declining AMH levels.

CONCLUSIONS

The similarity between observed and predictive distributions of age at menopause supports the hypothesis that AMH levels are related to onset of menopause. Results of this study suggest that AMH is able to specify a woman's reproductive age more realistically than chronological age alone.

Prevalence of premature ovarian failure in monozygotic and dizygotic twins

BACKGROUND

Premature ovarian failure (POF) before 40 years of age from natural causes affects approximately 1% of adult women, with minor variations between ethnic groups. A recent case of ovarian transplantation between young monozygotic (MZ) twins in which one had undergone unexplained POF at 14 years has prompted a study of the prevalence of POF.

METHODS

Menopausal ages of 832 Australian and UK female twin-pairs were extracted from volunteer national twin registry databases containing medical, reproductive and lifestyle data surveyed by mail questionnaire. Surgical menopause was an exclusion criterion.

RESULTS

The prevalence of POF in both MZ and dizygotic (DZ) twins was similar in both registries and 3- to 5-fold greater than the general population at age thresholds 40 and 45 years. No specific factors were found to account for the higher risk of early menopause. Some twins of both zygosities were highly discordant for menopausal age (>or=10 years). Nevertheless, there was significant intra-twin dependence, especially for MZ twins, and the average age difference at last menses was greater in DZ twin-pairs.

CONCLUSION

Both MZ and DZ twins are at higher risk of POF. Despite some striking differences within MZ twin-pairs, menopausal ages were more concordant than for DZ twin-pairs, confirming that the timing of menopause has a heritable component.

Modeling the Dependence between the Number of Trials and the Success Probability in Binary Trials

A model for binary trials based on a bivariate generalization of the Poisson process for both the number of successes and number of trials with the transition rates dependent on the accumulating numbers of successes and trials is used to reanalyze some recently published data of Zhu, Eickhoff, and Kaiser (2003, Biometrics59, 955-961). This modeling admits alternative distributions for the numbers of trials and the numbers of successes conditional on the number of trials which generalize the Poisson and binomial distributions, without some of the restrictions apparent in the beta-binomial-Poisson mixed modeling of Zhu et al. (2003). Some quite marked differences between the results of this analysis and those described in Zhu et al. (2003) are apparent.

Markov chain modelling for geriatric patient care

OBJECTIVES

To show that Markov chain modelling can be applied to data on geriatric patients and use these models to assess the effects of covariates.

METHODS

Phase-type distributions were fitted by maximum likelihood to data on times spent by the patients in hospital and in community-based care. Data on the different events that ended the patients' periods of care were used to estimate the dependence of the probabilities of these events on the phase from which the time in care ended. The age of the patients at admission to care and the year of admission were also included as covariates.

RESULTS

Differential effects of these covariates were shown on the various parameters of the fitted model, and interpretations of these effects made.

CONCLUSIONS

Models based on phase-type distributions were appropriate for describing times spent in care, as the ordered phases had an interpretable structure corresponding to increasing amounts of care being given.

Acquisition and loss of Porphyromonas gingivalis, Actinobacillus actinomycetemcomitans and Prevotella intermedia over a 5-year period: effect of a triclosan/copolymer dentifrice

OBJECTIVES

The present study describes the natural history of Porphyromonas gingivalis, Actinobacillus actinomycetemcomitans and Prevotella intermedia over a 5-year period and the effect of a triclosan/copolymer dentifrice on these organisms in a normal adult population.

MATERIAL AND METHODS

Subgingival plaque samples were collected from 504 adult volunteers. Probing pocket depths (PPD) and relative attachment levels were measured using an automated probe. Participants were matched for disease status (CPI), plaque index, age and gender, and allocated to receive either a triclosan/copolymer or placebo dentifrice. Re-examination and subgingival plaque sampling was repeated after 1, 2, 3, 4 and 5 years. P. gingivalis, A. actinomycetemcomitans and P. intermedia were detected and quantitated using an enzyme linked immunosorbent assay. Logistic regression and generalised linear modelling were used to analyse the data.

RESULTS

This 5-year longitudinal study showed considerable volatility in acquisition and loss (below the level of detection) of all three organisms in this population. Relatively few subjects had these organisms on multiple occasions. While P. gingivalis was related to loss of attachment and to PPD >/=3.5 mm, there was no relationship between A. actinomycetemcomitans or P. intermedia and disease progression over the 5 years of the study. Smokers with P. gingivalis had more PPD >/=3.5 mm than smokers without this organism. There was no significant effect of the triclosan dentifrice on P. gingivalis or A. actinomycetemcomitans. Subjects using triclosan were more likely to have P. intermedia than those not using the dentifrice; however this did not translate into these subjects having higher levels of P. intermedia and its presence was uniform showing no signs of increasing over the course of the study.

CONCLUSION

The present 5-year longitudinal study has shown the transient nature of colonisation with P. gingivalis, A. actinomycetemcomitans and P. intermedia in a normal adult population. The use of a triclosan-containing dentifrice did not lead to an overgrowth of these organisms. The clinical effect of the dentifrice would appear to be independent of its antimicrobial properties.

The effect of a triclosan-containing dentifrice on the progression of periodontal disease in an adult population

OBJECTIVES

The aim of the present study was to determine the effect of unsupervised, long-term use of a 0.3% triclosan/2% copolymer dentifrice on the progression of periodontal disease in a general adult population.

METHODS

Five hundred and four volunteers were enrolled in a double-blind, controlled clinical trial. Participants were matched for disease status, plaque index, age and gender. At the baseline examination, probing pocket depths and relative attachment levels were recorded and participants were assigned to either the test or control group. Re-examinations took place after 6, 12, 24, 36, 48 and 60 months. Subgingival plaque samples were collected at each examination and assayed for Porphyromonas gingivalis, Actinobacillus actinomycetemcomitans and Prevotella intermedia. A generalised linear model was used to analyse the data, with a number of covariates thought to influence the responses included as the possible confounding effects.

RESULTS

The triclosan/copolymer dentifrice had a significant effect in subjects with interproximal probing depths > or =3.5 mm, where it significantly reduced the number of sites with probing depths > or =3.5 mm at the following examination, when compared with the control group (p<0.001). Furthermore, this effect increased with increasing numbers of affected sites. There was no effect of the triclosan/copolymer dentifrice in individuals without probing depths > or =3.5 mm at the previous examination. Other factors significantly affecting probing pocket depths (PPD) included increasing age, smoking and presence of P. gingivalis. PPD > or =3.5 mm were positively associated with loss of attachment some 2 years later.

CONCLUSION

This study showed that in a normal adult population, unsupervised use of a triclosan/copolymer dentifrice is effective in slowing the progression of periodontal disease.

A longitudinal study of interleukin-1 gene polymorphisms and periodontal disease in a general adult population

BACKGROUND

Cross-sectional studies have demonstrated that a specific polymorphism (allele 2 of both IL-1A +4845 and IL-1B +3954) in the IL-1 gene cluster has been associated with an increased susceptibility to severe periodontal disease and to an increased bleeding tendency during periodontal maintenance. The aim of the present study was to investigate the relationship between IL-1 genotype and periodontitis in a prospective longitudinal study in an adult population of essentially European heritage.

METHODS

From an ongoing study of the Oral Care Research Programme of The University of Queensland, 295 subjects consented to genotyping for IL-1 allele 2 polymorphisms. Probing depths and relative attachment levels were recorded at baseline, 6, 12, 24, 36, 48 and 60 months using the Florida probe. Periodontitis progression at a given site was defined as attachment loss > or =2 mm at any observation period during the 5 years of the study and the extent of disease progression determined by the number of sites showing attachment loss. Porphyromonas gingivalis, Actinobacillus actinomycetemcomitans and Prevotella intermedia were detected using ELISA.

RESULTS

38.9% of the subjects were positive for the composite IL-1 genotype. A relationship between the IL-1 positive genotype and increased mean probing pocket depth in non-smokers greater than 50 years of age was found. Further, IL-1 genotype positive smokers and genotype positive subjects with P. gingivalis in their plaque had an increase in the number of probing depths > or =3.5 mm. There was a consistent trend for IL-1 genotype positive subjects to experience attachment loss when compared with IL-1 genotype negative subjects.

CONCLUSION

The results of this study have shown an interaction of the IL-1 positive genotype with age, smoking and P. gingivalis which suggests that IL-1 genotype is a contributory but non-essential risk factor for periodontal disease progression in this population.

Likelihood-based modeling and analysis of data underdispersed relative to the Poisson distribution

By using a generalization of the Poisson process, distributions can be constructed that show appropriate amounts of underdispersion relative to the Poisson distribution that may be apparent from observed data. These are then used to examine the differences between the distributions of numbers of fetal implants in mice corresponding to different doses of the herbicide 2,4,5-T.

Follicle dynamics during ovarian ageing

The human ovary is endowed at birth with a fixed number of primordial follicles which steadily declines throughout life as a result of atresia and recruitment towards ovulation. The pattern of this decline is not exponential, but more bi-exponential corresponding to a 'broken-stick' regression of logged total numbers of follicles against age. Such a model implies an abrupt change in the exponential rate of follicle loss at age 38 years, and is thus rather implausible biologically. A more refined model with an exponential rate of follicle loss that changes gradually throughout life also describes the data on declining follicle numbers but in addition leads to a distribution of age at menopause, corresponding to follicle numbers falling below a critical threshold, that shows quite remarkable agreement with independent data on menopausal ages of American women. When the follicles are classified into resting and growing stages, it is found that any changes in the consequent process of follicle development as the ovary ages relate mainly to the small resting follicles and not the larger growing ones.

Ante-dependence modeling in a longitudinal study of periodontal disease: the effect of age, gender, and smoking status

BACKGROUND

It is generally accepted that periodontal disease progresses by a series of bursts that are interspersed by periods of stability or even gain of attachment. In order to analyze longitudinal data on a patient's disease experience, it is necessary to use models which accommodate serial dependence. Ante-dependence between the results of a series of periodontal examinations over time can be modeled using a Markov chain. This model describes temporal changes in patients' levels of disease in terms of transition probabilities, which allow for both regression and progression of the disease. The aim of the present study was to demonstrate the use of a Markov chain model to analyze data from a longitudinal study investigating the progression of periodontal disease in an adult population.

METHODS

The study population consisted of 504 volunteers; however, only 456 were included in the analysis because the remaining 48 subjects did not give consecutive data. Subjects were examined at baseline, 6 months, and 1, 2, and 3 years. Probing depths (PD) were recorded using an automated probe. Disease was defined as four or more sites with PD > or = 4 mm. Markov chain modeling was used to determine the effect of age, gender, and smoking on the natural progression and regression (healing) of periodontal disease.

RESULTS

Smoking and increasing age had no effect on the progression of disease in this population, but did have a significant effect (P values < or = 0.05) in reducing the regression of disease; i.e., their effect on disease appears to be inhibition of the natural healing process. Gender had no significant effects.

CONCLUSIONS

These results demonstrate how ante-dependence modeling of longitudinal data can reveal effects that may not be immediately apparent from the data, with smoking and increasing age being seen to inhibit the healing process rather than promote disease progression.

Estimations of the efficacy and reliability of paternity assignments from DNA microsatellite analysis of multiple-sire matings

It is important for bovine DNA testing laboratories to provide the cattle industry with accurate estimates of the efficacy and reliability of DNA tests offered so that end users of this technology can adequately assess the cost-benefits of testing. To address these issues for bovine paternity testing, paternity exclusion probability estimates were obtained from breed panel data and were predictive of the efficacy of the DNA tests used in 39 multiple-sire mating groups, involving 5960 calves and 505 bulls. Paternity testing of these mating groups has demonstrated that the majority involve a variable proportion of unknown sires and this impacts on the reliability of sire allocation. Mathematical models based on binomial or beta-binomial probability distributions were used to estimate the reliability of single-sire allocations from multiple-sire matings involving unknown sires. Reliability of 98-99% is achieved when the exclusion probability is 0.99 or greater, after allowing for up to 20% unknown sires. When the exclusion probability drops below 0.90 and there are 20% unknown sires, the reliability is poor, bringing into question the benefits of testing. This highlights the need for DNA testing laboratories to offer paternity tests with an exclusion power of at least 99%.

Biological bases of premature ovarian failure

The ovary is endowed at birth with a fixed number of primordial follicles, which steadily dwindles throughout life as a result of atresia and recruitment towards ovulation. In addition to age, the number varies allometrically between species, larger and longer-lived animals tending to have more follicles initially and these disappear at a slower rate. A causal relationship between follicle depletion and menopause clearly exists, and there is a gradual acceleration of follicle wastage in the human ovary beginning more than a decade before the end of menstrual life. A mathematical model has provided confirmatory evidence of this relationship, and indicates that menopause is triggered by a threshold number of follicles which varies stochastically with a mean of 1100.

Permeation of human ovarian tissue with cryoprotective agents in preparation for cryopreservation

The recent improvements in the treatment of cancer by chemo- and radiotherapy have led to a significant increase in the survival rates of patients with malignant disease, but at the expense of distressing side effects. One major problem, especially for younger patients, is that aggressive therapy destroys a significant proportion of the follicular population, which can result in either temporary or permanent infertility. Freeze-banking pieces of ovarian cortex prior to treatment is one strategy for preserving fecundity. When the patient is in remission, fertility could, theoretically, be restored by autografting the thawed tissue at the orthotopic site or by growing isolated follicles to maturity in vitro. Recent studies have found good follicular survival in frozen-thawed human ovarian tissue but to optimize the process an effective cryopreservation method needs to be developed. An essential part of such a technique is to permeate the tissue with a cryoprotectant to minimize ice formation and the extent of this equilibration is an important determinant of post-thaw cellular survival. In the current study, we have investigated the diffusion of four cryoprotective agents into human tissue at both 4 degrees C and 37 degrees C. We have also studied the effect of adding different concentrations of the non penetrating cryoprotective agent, sucrose, to the freezing media using the release of lactate dehydrogenase as a measure of its protective effect. At 4 degrees C propylene glycol and glycerol penetrated the tissue significantly slower than either ethylene glycol or dimethyl sulphoxide. At the higher temperature of 37 degrees C all four cryoprotectants penetrated at a faster rate, however concern about enhanced toxicity prevents the use of these conditions in practice. Thus, the results suggest that the best method of preparing tissue for freezing is exposure for 30 min to 1.5 M solutions of ethylene glycol or dimethyl sulphoxide at 4 degrees C; this achieved a mean tissue concentration that was almost 80% that of the bathing solution. We also report that the addition of low concentrations of sucrose to the freezing medium does not have a significant protective effect against freezing injury.

Impact of congenital or experimental hypogonadotrophism on the radiation sensitivity of the mouse ovary

As the numbers of young people making a full recovery from haematological malignancy continue to rise, reproductive science must investigate ways of ameliorating the sterilizing effects of high-dose chemotherapy and total body irradiation. Because there is conflicting evidence as to whether lower serum gonadotrophin concentrations have any protective effect on the gonads, a study was designed to test whether either congenital or experimentally induced hypogonadism reduces the radiosensitivity of the mouse ovary. Test subjects were either homozygous for the hpg locus or animals of normal phenotype treated with a gonadotrophin-releasing hormone antagonist. At 14 days after receiving a single dose of 0.1, 0.2 or 0.3 Gy X-rays or a sham procedure, primordial follicles in the ovaries of the two experimental groups and controls were counted in serial histological sections. The doses at which half of the follicles were lost (LD50) were estimated as 0.11 +/- 0.02, 0.19 +/- 0.02 and 0.17 +/- 0.02 Gy respectively. There was no significant difference between the controls and the antagonist-treated animals, but the congenitally hypogonadal group was unexpectedly more sensitive to radiation. Either way, these results do not support the hypothesis that the ovary is protected from radiation injury by lower gonadotrophin concentrations.

Efficacy of a dentifrice and oral rinse containing sanguinaria extract in conjunction with initial periodontal therapy

In the treatment of periodontal disease initial therapy aims at reducing marginal inflammation so allowing assessment of residual disease and further treatment options. The aim of the present study was to determine whether the use of a dentifrice and oral rinse containing sanguinaria extract led to a more rapid resolution of gingival inflammation following initial therapy. Thirty-four subjects, randomly assigned to one of two treatment groups, took part in this randomized double-blind parallel study. All subjects received initial therapy including oral hygiene instruction and scaling and root planing as required. One group also received an active dentifrice and oral rinse containing sanguinaria extract (an antiplaque agent) and zinc chloride. The other group received a placebo dentifrice and oral rinse. The gingival index (GI), plaque index (PLI) and probing pocket depths (PD) were recorded at six sites per tooth at baseline, two weeks after initial therapy and six weeks after initial therapy. There was no significant difference between the groups for any of the parameters at the baseline examination. Two weeks following initial therapy both groups showed a statistically significant increase in the number of sites with PLI of 0 or 1 (p < 0.0001) and a statistically significant increase in the number of sites with a GI of 0 or 1 (that is, no bleeding on probing), (p < 0.0001). Also there was a statistically significant increase in the number of sites with probing depths < or = 3 mm (p < 0.0001) compared with baseline. These changes were maintained through to six weeks post therapy. There was no significant advantage to the sanguinaria group. Results demonstrate that initial therapy in the form of oral hygiene instruction, scaling and root planing leads to a significant improvement in periodontal status which is maintained at least in the short term. Further, use of a dentifrice and oral rinse containing sanguinaria did not improve the efficacy of initial therapy.

Regression pattern of beta human chorionic gonadotrophin in blood after chemotherapy for gestational trophoblastic neoplasia

Although beta human chorionic gonadotrophin (beta-HCG) is a clinically-useful tumour marker in gestational trophoblastic neoplasia, there is limited information on how serum beta HCG regresses in molar pregnancy and choriocarcinoma during chemotherapy. The study included 41 patients who had been treated by single- and multidrug regimens, and decay curves for regression of beta HCG in the circulation in these patients were fitted to the data. Thirty-three patients achieved a biochemical remission ('cured') by first-line chemotherapy; this gave an overall efficacy rate of 80%. The beta HCG decay curves convey useful information of the chemosensitivity of the tumour, and may assist in determining the time required for treatment and earlier change in treatment for the chemoresistant tumour.

A model conforming the decline in follicle numbers to the age of menopause in women

The store of primordial follicles in the ovary is fixed before birth and dwindles with age until it is unable to provide enough Graafian stages to sustain menstrual cyclicity. According to a simple bi-exponential model of ageing, the rate of follicle disappearance increases at age 37.5 years (or when 25 000 follicles remain) so that the numbers fall to approximately 1000 at 51 years, the median age of menopause in the population. This study attempts to produce a biologically more realistic model of follicle disappearance and harmonizes follicle dynamics with the distribution of menopausal ages from an American survey. The step-change in the rate of follicle attrition was replaced by a model which assumed that this rate changes more gradually with the size of the follicle store. This produced a distribution of predicted menopausal ages (based on an assumed threshold of 1000 follicles) which was closer to observed data. The fit further improved when the model was modified by having a threshold that varied across the population. Using such a stochastic threshold model for menopause, the number of fertile years remaining could be forecast with an acceptable margin of uncertainty if it ever becomes possible to estimate the size of the follicle store in vivo.

A mathematical model of follicle dynamics in the human ovary

A mathematical model has been developed to describe the rates of growth and death of follicles in human ovaries between 19 and 50 years of age. It was based on the numbers of follicles at three successive stages of development, which were obtained by counting follicles in histological sections of ovaries from 52 normal women. The model indicated that follicle dynamics were age dependent, with a transition at 38 years of age when the rate of follicle disappearance increased. The rates of follicle growth increased at successive stages but did not change with age. The annual egress from stage III (consisting of follicles with two or more granulosa cell layers) was affected by the declining numbers of small follicles, and corresponded to 31, nine and one follicles per day at 29-30, 39-40 and 49-50 years of age respectively. The rate of death at stage I (representing small, resting follicles) was the only parameter which varied significantly with age: no evidence of significant atresia was found for this stage in ovaries < or = 38 years old, but there was significant death above this age. As a consequence, only 40% of follicles leaving stage I reached stage III in older ovaries and just 1500 follicles in toto remained at 50 years of age from the 300,000 present at 19 years. This high death rate of small follicles appears to be responsible for advancing the timing of ovarian failure, and therefore of menopause, to midlife in our species.

Ovarian aging, follicular depletion, and steroidogenesis

The follicular population. Menopause occurs as a consequence of the continuous utilization of a fixed store of primordial follicles leading to almost total depletion at mid-life or sometimes earlier. The great majority of follicles that disappear are lost by atresia rather than by ovulation, and the rate of loss accelerates in the last decade of menstrual life. The numbers of growing follicles at a given age are correlated with those of the primordial stages, but there are always more being recruited than required for a single ovulation each month. The extent to which a dwindling number is responsible for the character of cycles of the menopausal transition remains unclear. Ovarian secretion. While menstrual cycles remain regular, circulating concentrations of estradiol and progesterone are relatively independent of age. On the other hand, serum levels of inhibin are substantially lower in women approaching menopausal age, probably reflecting smaller numbers of growing follicles at the beginning of the cycle. Alleviation of negative feedback on the pituitary gland results in a greater output of follicle-stimulating hormone (FSH), but the effects of chronic superstimulation on the aging ovary are not known. Follicular aging. Aging of long-lived oocytes could affect the developmental potential of the follicle unit as well as compromising the chances of late pregnancy. Another important field of investigation is therefore to determine the balance of responsibility between cumulated damage to molecules by toxins, on the one hand, and the effects of physiological aging and such epiphenomena as the changing hormonal or paracrine environments, on the other.

A structured compartmental model for drug kinetics

A compartmental model with a structure that describes drug kinetics by incorporating the ideas of diffusion and gamma distributed clearance times is proposed. The equations describing this model may be solved by elementary numerical techniques, and the model is shown to fit a data set describing renal gentamicin concentrations, better than a simple power-function model.

Diffusion approximations for stochastic compartmental models

A diffusion approximation is developed for one-compartment systems with nonlinear elimination rates. Both impulsive input and continuous infusion are considered. Explicit expressions for the mean and autocovariance functions of the contents of the compartment as time elapses are given.

Accelerated disappearance of ovarian follicles in mid-life: implications for forecasting menopause

Menopause is triggered by the number of ovarian follicles falling below a threshold number and is irreversible because oogonial stem cells disappear after birth. Since it is the result of programmed disappearance of a limited store of follicles, menopause can be predicted using mathematical models based on total follicle counts at different ages. Our model shows follicle numbers decline bi-exponentially rather than as a simple exponential function of age, as had been assumed, with a first exponential rate parameter of -0.097 and a second of -0.237. The change occurred when numbers had fallen to the critical figure of 25,000 at age 37.5 years. The unexpectedly faster rate of ovarian ageing afterwards lowers the follicle population to 1000 at approximately 51 years, and was adopted as the menopausal threshold because it corresponds to the median age of menopause in the general population. Had the earlier rate persisted menopause would not be expected until 71 years. The impact of step reductions of follicle numbers on the prospective span of menstrual life was predicted by the model. A reduction by 50% before age 30 years resulted in the threshold being reached at 44 years and 0.6 year later for every subsequent year until age 37.5 years after which it is reached at 48 years. A reduction of 90% in childhood before age 14 years could result in menopause as early as 27 years, with increments of 0.6 year per year afterwards until after 37.5 years when it is expected at age 41 years.(ABSTRACT TRUNCATED AT 250 WORDS)

Impact of exogenous progesterone on ovarian follicular dynamics and function in mice

Raising progesterone concentrations in young adult mice by subcutaneous implants resulted in ovulation being blocked and the cessation of oestrous cycles. The effect of this treatment on the numbers and dynamics of preantral follicles during 36 days of treatment was studied using a compartmental model to analyse differential follicle counts. Changes in growth and/or death rates were detected at all stages of follicular development. An increased rate of growth through preantral stages was predicted in the treatment group when compared with the controls, but most of these follicles did not reach the antral stage of development as an increased death rate was observed at large preantral stages (stage IV). Antral follicles were formed in the treatment group, but all succumbed to atresia. Increased atresia in the antral population of follicles in the treatment group was observed directly.

Ovarian cyclicity and follicular recruitment in unilaterally ovariectomized mice

Halving the numbers of follicles in young adult mice by unilateral ovariectomy resulted in compensatory Graafian follicle growth with a reduction by about 25% of the expected number of oestrous cycles. The impact of the operation on the numbers and dynamics of preantral follicles during the first 2 months after ovariectomy was studied using a compartmental mathematical model to analyse differential follicle counts. There were changes in growth and/or death rates at all stages of follicle development, and the patterns emerging were time-dependent. The rate of follicle survival from the pool of unilaminar stages was paradoxically reduced, but those forming two granulosa cell layers continued to develop towards Graafian size. As the frequency of follicle death declined, the numbers of healthy large preantral and antral stages in unpaired ovaries rose to approach those in pairs of age-matched control ovaries, suggesting that follicles otherwise undergoing atresia were being rescued. In the long-term, follicle dynamics after unilateral ovariectomy at young ages did not appear to compromise fecundity seriously.